Chapter 11.1, Problem 5E

To determine

Tocomplete:The statement “The midpoint of the line segment joining the points $\left(x_1,y_1,z_1\right)$ and $\left(x_2,y_2,z_2\right)$ given by the Midpoint Formula in Space is _______.”

Answer to Problem 5E

  $\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2},\frac{z_1+z_2}{2}\right)$

Explanation of Solution

Given information:

The give statement is “The midpoint of the line segment joining the points $\left(x_1,y_1,z_1\right)$ and $\left(x_2,y_2,z_2\right)$ given by the Midpoint Formula in Space is _______.”

The midpoint between the two points can be calculated by the midpoint formula in space. Let’s there are two points $\left(x_1,y_1,z_1\right)$ and $\left(x_2,y_2,z_2\right)$ are given in a three-dimensional coordinate system.

The midpoint between the points $\left(x_1,y_1,z_1\right)$ and $\left(x_2,y_2,z_2\right)$ can be calculated as follows.

  $\text{Midpoint}=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2},\frac{z_1+z_2}{2}\right)$